Nodal high-order methods on unstructured grids. I: Time-domain solution of Maxwell's equations
type: Item
instance of: scholarly article
title: Nodal high-order methods on unstructured grids. I: Time-domain solution of Maxwell's equations
zbMATH Open document ID: 1014.78016
published in: Journal of Computational Physics
publication date: 2002-12-16T00:00:00Z
review text: The paper presents a high-order convergent method for the solution of the time-dependent Maxwell equations in geometrically complex domains. The spatial discretization on the unstructured tetrahedral mesh uses a high order nodal basis of multivariate Lagrange polynomials. The discrete equations are satisfied in a discontinuous Galerkin-Petrov form with the boundary and transmission conditions enforced weakly through a penalty term. The authors prove stability and convergence of the semidiscrete approximation to Maxwell's equations and establish an error estimate of at most linear growth in time. The results can be applied to the solution of linear conservation laws. The authors present a number of numerical examples to verify the theoretical results and to illustrate the efficiency and robustness of the method when solving benchmark problems in computational electromagnetics. Problems of the efficient implementation and parallel performance are discussed.
reviewed by: Gunther Schmidt
Mathematics Subject Classification ID: 78M25
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 1845971
zbMATH Keywords: high-order convergence
zbMATH Keywords: spectral methods
zbMATH Keywords: stability
zbMATH Keywords: unstructured grids
zbMATH Keywords: Maxwell's equation
author: Jan S. Hesthaven
author: T. Warburton
describes a project that uses: BLAS
describes a project that uses: MPI
MaRDI profile type: Publication
full work available at URL: jcph.2002.7118
OpenAlex ID: W2017488448
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DOI: 10.1006/JCPH.2002.7118
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Nodal high-order methods on unstructured grids. I: Time-domain solution of Maxwell's equations (cites work)
cites work: Nodal high-order methods on unstructured grids. I: Time-domain solution of Maxwell's equations